MATHEMATICS AND STATISTICS haverford.edu/mathematics The courses in the Department of Mathematics the requirements, but are of course prerequisites and Statistics aim to: for all subsequent courses in mathematics. • promote rigorous thinking in a systematic, deductive, intellectual discipline. Intermediate Calculus/Linear Algebra • help students identify and articulate This category includes MATH 215, 121 or 216. mathematical and statistical problems that These courses are taught for the benefit of both they encounter, both in formal academic work majors and non-majors, but are the real and elsewhere. “introduction” to math for most majors. • foster technical competence in mathematics and statistics as an aid to the better Core Major Courses comprehension of the physical, biological, and This category includes MATH 317-318 (Analysis) social sciences. and MATH 333-334 (Algebra). These courses are • guide and direct majors toward an interest in the “cornerstone” of the major, introducing many research in the mathematical and statistical important ideas in which modern mathematics is sciences. based, and also sharpening students’ skills in mathematical discourse (i.e., careful statements of definitions, theorems, proofs). LEARNING GOALS Students taking courses in the Department of Intermediate Electives Mathematics and Statistics will think rigorously • MATH 203 (Statistical Methods and Their and systematically both within the context of the Applications) discipline and in its applications—and, ideally, throughout the liberal arts curriculum. Students • MATH 204 (Differential Equations) will learn to identify and articulate mathematical • MATH 210 (Linear Optimization and Game problems that they encounter, both in Theory) mathematics and in other disciplines. Students • MATH 218 (Probability) will develop skills necessary to engage these • MATH 222 (Introduction to Scientific problems within a mathematical and/or Computing) statistical framework. Finally, students will learn • MATH/CMSC 235 (Information and Coding how to communicate their mathematical and Theory) statistical findings to a variety of audiences. • MATH 286 (Applied Multivariate Statistical Analysis). CURRICULUM Mathematics majors take a three-year core These courses are designed for both majors and sequence of courses in calculus, linear algebra, non-majors, and provide majors an excellent abstract algebra, and analysis, designed to opportunity to explore interests outside the core provide a foundation for further study in the sequence. Students can expect at least two major areas of modern mathematics. Students electives at this level to be offered most with substantial advanced placement may semesters. We coordinate with Bryn Mawr so that complete this sequence by the end of their if a topic is not offered in a given year at sophomore year. Students who have completed Haverford, it may be offered at Bryn Mawr. the core sequence may take advanced courses in algebra, analysis, topology, or other special Advanced Electives: topics. • MATH 328 (Mathematical Statistics) • MATH 335-336 (Topology) Mathematics courses for majors fall into six • MATH/CMSC 340 (Analysis of Algorithms) general categories: • MATH/CMSC 345 (Theory of Computation) • MATH 390 (Advanced Topics in Algebra) Preliminary Calculus • MATH 391 (Advanced Topics in Geometry This category includes MATH 105, 118, or and Topology) advanced placement. These are not listed among • MATH 392 (Advanced Topics in Analysis) Haverford College Catalog 2017-2018 275 MATHEMATICS AND STATISTICS • MATH 394 (Advanced Topics in Discrete substitute equivalent courses in mathematics at Math and Computer Science) Bryn Mawr College for any requirement, subject • MATH 395 (Advanced Topics in to advisor approval. Combinatorics) • MATH 396 (Advanced Topics in Probability MINOR REQUIREMENTS and Statistics) Mathematics minors take the same core sequence • MATH 397 (Advanced Topics in Applied as do the majors, though not necessarily to the Mathematics) same depth, followed by a selection of electives tailored to the student’s interest. Statistics minors Courses at this level are very important for take a separate core sequence in probability and students planning to go to graduate school in statistics, with later flexibility in pursuing either a mathematics or related fields. The department more applied or a more theoretical track. typically offers five to six courses at this level per year. Mathematics Minor Requirements • MATH 215 (Linear Algebra) and either MATH Other Courses: 121 (Multivariable calculus) or MATH 216 • MATH 399 (Senior Seminar): a required (Advanced Calculus). year-long group seminar for seniors that • MATH 317 (Analysis I) and MATH 333 offers advice, support, and practice in (Algebra I). preparing the senior paper and oral • Two additional electives in mathematics at the presentation. 200 level or higher. • MATH 400 (Senior Research): a required year-long course for seniors that involves Minors may substitute equivalent courses in independent work with their senior thesis mathematics at Bryn Mawr College for any advisor. requirement, subject to advisor approval. • MATH 460 (Teaching Assistantship in Mathematics): a half-credit course, in which Statistics Minor Requirements students work closely with a single faculty • One of the following courses (Introduction to member in a single course at the 100 or 200 Statistics): STAT 203, ECON 204, PSYC 200, level, offering various kinds of classroom SOCL 215 support including problem sessions, review, • STAT 286 (Applied Multivariate Statistical tutoring, and laboratory assistance. Very good Analysis) experience for students considering teaching • MATH 218 (Probability) as a career. Open to junior and senior majors • MATH 215 (Linear Algebra) by invitation, and may be taken at most twice. • MATH 121 or MATH 216 (Multivariable Does not count toward the major. Calculus) • One of the following: MAJOR REQUIREMENTS o STAT 328 (Mathematical Statistics) • MATH 215, and either MATH 121 or MATH o STAT 396 (Advanced Topics in Probability 216. and Statistics) • MATH 317 and 333, and one of MATH 318 or o ECON 304 (Econometrics) 334. o SOCL 320 (Advanced Quantitative • Four additional electives in mathematics or Methods for Sociologists). approved related courses at the 200 level or higher. At least one of these must be at the Options for the Statistics Minor 300 level. (Note: MATH 399, MATH 400, • A math minor can also be a statistics minor. If MATH 460, and MATH 480 do not count a student wants to be a math minor and a toward this requirement.) statistics minor, the following courses: STAT • The senior seminar, fall and spring. 203, ECON 204, MATH 218, STAT 286, STAT • A senior paper and oral presentation. 328 and STAT 396, cannot be counted to satisfy both the math minor and statistics We strongly advise students planning graduate minor. study in mathematics or related fields to take • A math major can also be a statistics minor. If additional courses at the 300 level. Majors may a student wants to be a math major and a 276 Haverford College Catalog 2017-2018 MATHEMATICS AND STATISTICS statistics minor, the following apply: students. o STAT 203, ECON 204 and STAT 286 cannot be counted to satisfy both the math Senior Project Learning Goals major and statistics minor requirement. Our students will engage with advanced content o At most one of the following courses can and techniques in pure mathematics, applied be counted to satisfy both the math major mathematics and statistics. They will gain and statistics minor: MATH 218, STAT ownership of the process and material through 328 and STAT 396. understanding the content and the details of the • Math majors with economics concentration: problem they are investigating, constructing If a math major wants to be an econ illustrative examples, carrying out novel concentrator and a statistics minor, MATH computations or carefully analyzing a data set. 218, STAT 286, STAT 328 and STAT 396 Our students will write clear, careful and correct cannot be counted toward both the economics mathematics/statistics, from precise definition or concentration and the statistics minor. description of a model to rigorous proofs or well- • Economics majors with math concentration: supported analyses. They will develop an oral If an economics major wants to be a math presentation that highlights the central ideas of concentrator and also a statistics minor, the their thesis work at a level appropriate for an following apply: audience in the mathematical/statistical sciences. o MATH 218, STAT 286, STAT 328 and STAT 396 cannot be counted to satisfy Senior Project Assessment both the stat minor and the math The grade for the senior thesis is determined by concentration requirement. the following: o ECON 304 cannot be counted toward the • Level of engagement with advanced statistics minor. (ECON 304 is required by mathematics or statistics. the economics major.) • Level of ownership of the material and of the writing process. For further information about the statistics • Adherence to professional standards of minor, please see the PDF supplement on the written mathematics and statistics. mathematics website, or contact the minor coordinator. The grade for the senior seminar is determined by the following: SENIOR PROJECT • Completing all the assignments in accordance A senior paper is written by each major in close with the assignment description. coordination with a faculty member. The senior • Meeting deadlines for each assignment. paper is a year-long